applied sciences Article Broadband Strong-Motion Prediction for Future Nankai-Trough Earthquakes Using Statistical Green’s Function Method and Subsequent Building Damage Evaluation Baoyintu 1, Naren Mandula 2 and Hiroshi Kawase 3,* 1 Transportation Institute, Inner Mongolia University, Inner Mongolia 010070, China; [email protected] 2 College of Geographical Science, Inner Mongolia Normal University, Inner Mongolia 010022, China; [email protected] 3 DPRI, Kyoto University, Kyoto 606-0011, Japan * Correspondence: [email protected]; Tel.: +81-774-38-4052 Featured Application: The proposed method is applicable to the quantitative earthquake disaster impact evaluations in the areas of high seismic risk. Abstract: We used the Green’s function summation method together with the randomly perturbed asperity sources to sum up broadband statistical Green’s functions of a moderate-size source and predict strong ground motions due to the expected M8.1 to 8.7 Nankai-Trough earthquakes along the southern coast of western Japan. We successfully simulated seismic intensity distributions similar to the past earthquakes and strong ground motions similar to the empirical attenuation relations of peak ground acceleration and velocity. Using these results, we predicted building damage by non-linear response analyses and find that at the regions close to the source, as well as regions with Citation: Baoyintu; Mandula, N.; relatively thick, soft sediments such as the shoreline and alluvium valleys along the rivers, there is a Kawase, H. Broadband possibility of severe damage regardless of the types of buildings. Moreover, the predicted damage Strong-Motion Prediction for Future ratios for buildings built before 1981 are much higher than those built after because of the significant Nankai-Trough Earthquakes Using code modifications in 1981. We also find that the damage ratio is highest for steel buildings, followed Statistical Green’s Function Method by wooden houses, and then reinforced concrete buildings. and Subsequent Building Damage Evaluation. Appl. Sci. 2021, 11, 7041. https://doi.org/10.3390/app11157041 Keywords: strong motion; Green’s function summation; asperity; ground motion modeling; damage prediction; subduction-zone earthquake; Nankai-Trough Academic Editor: Guido Ventura Received: 29 June 2021 Accepted: 26 July 2021 1. Introduction Published: 30 July 2021 Off the Pacific coast of Tohoku, Japan, an earthquake of Mw 9.0 struck at 2:46 p.m., 11 March 2011, in the large regions of northeastern Japan. The ruptured area of this mega- Publisher’s Note: MDPI stays neutral thrust earthquake spanned a wide region from offshore Sanriku to offshore Ibaraki areas of with regard to jurisdictional claims in the Pacific coast of Japan. More than 22,000 people were killed or missing, primarily due to published maps and institutional affil- the tsunami, and devastating damage was incurred, particularly along the Pacific coast of iations. Tohoku. Although such massive M9-class earthquakes are expected to occur very infre- quently, typical M8-class subduction-zone earthquakes have a relatively high probability of happening and still, a wide region in the order of a few hundred kilometers will be affected. In addition to the direct damage, such as casualties and building damage from strong Copyright: © 2021 by the authors. ground motions, landslides, liquefaction, subsidence, and tsunami, there is secondary Licensee MDPI, Basel, Switzerland. damage including fires, damage to industrial facilities, and disruption of transportation. As This article is an open access article a result, the economy will be affected at the national level. The hypocenters are distributed distributed under the terms and along the Pacific coast of the Japanese islands, and taking earthquake disaster prevention conditions of the Creative Commons measures suitable for each region is considered an urgent task all over Japan. Attribution (CC BY) license (https:// The possibility that a mega-thrust earthquake of a separated segment at the Tokai, creativecommons.org/licenses/by/ Tonankai, or Nankai region along the Nankai Trough will happen within the next 30 years 4.0/). Appl. Sci. 2021, 11, 7041. https://doi.org/10.3390/app11157041 https://www.mdpi.com/journal/applsci Appl. Sci. 2021, 11, 7041 2 of 24 is estimated to be around 70~80% [1]. If one happens, severe damage by strong shaking and the subsequent tsunami is anticipated over a wide area, especially at the Pacific coast from the Tokai to Kyushu regions near the subducting Philippine Sea plate. To consider effective countermeasures, damage prediction that considers strong-motion characteristics and their building response is necessary to quantitatively evaluate the impact of the building damage from hypothesized earthquake scenarios that could happen in the future. There are still many old buildings that do not have sufficient earthquake resistance capacities in Japan. Grasping earthquake resistance performance of these actual buildings to predict damage is very important. Rigorous investigations after the 1995 Hyogo-ken Nanbu earthquake made damage prediction with considerable accuracy possible (e.g., Nagato and Kawase [2–4], Matsushima and Kawase [5,6]). However, several issues remain when predicting strong ground motions of subduction-zone earthquakes; for example, how to express the complex rupture process that can contribute various characteristics of strong ground motions in a wide frequency range. Moreover, the extremely important component to evaluate total damage using a quantitative damage prediction model of structures, rather than the conventional vulnerability function approach [7], and take damage mitigation measures based on the structural-type dependent evaluation is currently far from quantitative. For strong motion prediction, various methods have been developed toward a more quantitative prediction for a wider range of frequencies. As a gross categorization, we have theoretical methods, semi-empirical methods, and empirical methods. The accuracy of the theoretical methods depends on the accuracy of the velocity model used, which may need significant efforts to predict ground motions in a broadband frequency range [8,9]. The accuracy of the empirical method, such as the ground motion prediction equation (GMPE) [10,11], depends on the density of the observed data that constrain empirical relationships. Because of the infrequent occurrence of mega-thrust events, the density of observed data with large magnitude is far from ideal. In this regard, the semi-empirical method where moderate-sized earthquake ground motions are used as empirical Green’s functions and the summation with space and time are performed to predict strong motions from a mega-thrust event would be the best, for its broadband characteristics are based on the observed ground motions and the abundance of observed data to choose from [12–16]. Therefore, we follow them with different representations of the statistical Green’s function used. First, quantitative prediction of strong ground motions in a wide frequency range is provided based on the Green’s function summation technique using a statistical Green’s function valid from as low as 0.1 Hz up to 20 Hz derived from the observed strong motions in Japan [17]. Subduction-zone mega-thrust earthquakes along the Nankai Trough attract much concern and may lead to a chain rupture to adjacent fault segments (cascade model). Therefore, strong ground motions from hypothesized individual and chain ruptures of the Tokai, Tonankai, and Nankai segments in southwestern Japan are predicted in this paper. The predicted strong ground motions are compared with the seismic intensity distributions of past earthquakes. Their peak values in acceleration and velocity are also compared with empirical predictions from the well-calibrated GMPE [10]. Second, the predicted strong ground motions are used to estimate the damage of building structures using nonlinear response analysis models reflecting the characteristics of the seismic input and building types and their construction ages [2–4]. Finally, the merit of the proposed procedure for building damage prediction is discussed with special reference to the retrofitting policies for earthquake resistance performance of existing buildings based on the findings in this paper. 2. Development of a Statistical Green’s Function To predict strong ground motions over a wide frequency range, Ho and Kawase [17] developed a method to create a statistical Green’s function that is valid in the frequency range from 0.12 to 20 Hz based on the strong motion database in Japan. Their empirical modeling of the dataset based on the generalized inversion technique of Kawase and Matsuo [18] covered the entirety of Japan and investigated 110 earthquakes (with 25 inland Appl. Sci. 2021, 11, 7041 3 of 24 earthquakes, 34 subduction-zone intraplate earthquakes, and 51 subduction-zone interplate earthquakes) between August 1996 and March 2005, where the magnitude M ≥ 5.5, the hypocentral depth ≤ 60 km, the maximum acceleration ≤ 200 cm/s2, and the maximum distance to a hypocenter ≤ 400 km. Crustal earthquakes are defined by a hypocentral depth less than 25 km and an inland hypocenter location. Plate-boundary earthquakes have a hypocentral depth of more than 25 km, are low-angle reverse fault according to the fault mechanism solution by Harvard CMT [19] (before 1997) or F-net [20] (after 1997), and the slip direction is along the plate motion. The intraplate earthquakes have a hypocentral